Entropy measures the number of ways a system can be arranged while looking the same from the outside.
A "sorted" state (all hot particles on one side) has very few arrangements. A "mixed" state has astronomically more.
"The growth of entropy is nothing more than the natural tendency of things to go from rare configurations to more probable ones."
This is why:
• Heat flows from hot to cold (not the reverse)
• Ice cubes melt in warm water
• Eggs break but don't unbreak
• Time seems to flow forward
The "arrow of time" itself comes from entropy. We remember the past (low entropy) and not the future (high entropy).
Heat is just the random motion of particles. When fast (hot) particles collide with slow (cold) ones, they share energy until everything is the same temperature — the most probable state.